Multiplication with parentheses

Do you remember the order of operations? We usually say that parenthesis come before multiplication. This is a good rule for a beginner but now it's the time to see what you really do when you multiply expressions in parenthesis. Here's a problem where you need to multiply two expressions in parenthesis, but you can't calculate the expressions first because you don't know the value of x. We presented the multiplication as a rectangle with the sides lengths as the factors.

Now look what happens if we split the rectangle into 4 parts. We can calculate the area of each part separately. 3 times x is 3x. 3 times 2 is 6. x times x is x².

x times 2 is 2x. Each of the terms is now multiplied by each of the terms inside the other parenthesis. Now you can gather similar terms, that is those that have the same power of the variable. 3x + 2x is 5x. The multiplication is done.

When multiplying parenthesis you don't need to draw a rectangles like we just did. It's enough to follow this formula. Take the first term in the first parenthesis. Multiply it by each of the terms in the second parenthesis. Take the next term in the first parenthesis and do the same.

Continue until each term from the first parenthesis is multiplied by each term from the second parenthesis. Here is another example: this time there is subtraction as well, so watch out. (4 + x) x (x - 2) 4 times x is 4x. 4 x -2 is -8. x times x is x². x times -2 is -2x.

Gather the similar terms. 4x - 2x is 2x, which leaves us with 2x -8 + x² - done. The formula or algorithm that you follow is simple. Each term should be multiplied by each of the terms inside the other parenthesis. But there are many steps to keep track of, and it's easy to miss one of them, so be accurate, and mark the combinations you have already multiplied.

You now know that expressions in the parenthesis don't have to be calculated beforehand if you know how to multiply them.